The Optimal Mix of Bank and Market Debt:An Asset Pricing Approach∗Dirk Hackbarth Christopher A. Hennessy Hayne E. LelandFebruary 5, 2003ABSTRACTThis paper examines the optimal mix and priority structure of bank and market debt using atax shield-bankruptcy cost tradeoff model where the only unique feature of banks is their abilityto renegotiate. Closed-form expressions are derived for the values of renegotiable bank debt,non-renegotiable market debt, equity, and levered firm values. Optimal debt structure hingesupon ex post bargaining power. Weak firms utilize bank debt exclusively. Strong firms use amixture of bank and market debt, with bank debt senior. The model explains: (i) why smallfirms use bank debt exclusively; (ii) why large firms employ mixed debt financing; (iii) wh ybank debt is senior; and (iv) why firms shift from bank debt into a mixture of market and bankdebt over their life-cycle. The optimal debt contracts entail Absolute Priority, and we provideestimates of the cost of ex post priority violations across creditor classes.JEL Codes: G13, G32, G33.Keywor ds: Banking, Capital Structure, Priority Structure, and Contingent Claims Pricing.∗Walter A. Haas School of Business, U.C. Berkeley. We would like to thank seminar participants at the Universityof Arizona, U.C. Berkeley, and Stanford University where early versions of this paper were presen ted. Special thanksto Paul Pfleiderer for detailed comments and suggestions.I. IntroductionFollo wing Modigliani and Miller’s (1958) irrelevance result, the corporate tax shield provided bydebt was cited as an importan t determinant of capital structure. More recently, contract theoristshave questioned the utility of the tax shield in resolving the capital structure puzzle. For instance,Hart and Moore (1995) argue that, “these approaches cannot explain the types of debt claimsobserved in practice.”1This paper demonstrates that reports of the tax shield’s demise arepremature, and that, in fact, the debt tax shield is sufficient to explain many of the stylized factswith respect to debt structure that are central to the banking and cont racting literatures.The optimal debt structure maximizes ex ante firm value. Employing a continuous-time assetpricing framework, we paper identify the optimal priority structure and mixture of renegotiabledebt (bank and privately placed debt) and non-renegotiable (market) debt.2Debt mix and prioritystructure determine the value of tax shields, bankruptcy costs, and renegotiation costs. Analyticalsolutions are derived for bank debt, market debt, equity, and levered firm values as functions ofthe endogenous variables (promised coupons and priorit y structure) and exogenous parameters (expost bargaining power, underlying v olatility, tax rates, renegotiation costs, and bankruptcy costs).Absolute Priority (AP) across creditor classes is optimal in our setting, and we estimate the exante costs of anticipated deviations from AP across creditor classes.Optimal debt structure hinges upon the division of ex post bargaining power between the firmand bank. We consider two polar cases. Strong Firms have full bargaining power in renegotiationsand engage in strategic default, making take-it-or-leave-it offers over debt service and capturing allbilateral surplus.3In contrast, Weak Firms receive take-it-or-leave-it offers from the bank inrenegotiations, implying the bank extracts all bilateral surplus. For this reason, we label the bankdebt obligations of strong and weak firms Equity Power Debt (EPD) and Bank Power Debt (BPD),respectively. In the model, firms can choose the optimal mix of market and bank debt, but cannotchoosethetypeofbankdebttheyissue. Thatis, in terms of their bank debt commitments,strong and weak firms are constrained to issue EPD and BPD, respectively. Bargaining power istreated as a “fact of life” for the firm, since an agreement to be weak is not incentive compatible1Hart (1993) makes the same argument.2The term “bank debt” is adopted as a shorthand for all renegotiable debt including private placements.3The term strategic default is borrowed from Anderson and Sundaresan (1996) and Mella-Barral and Perraudin(1997).1ex post. It is most natural to think of weak firms as being relatively small or y oung corporationsthat are possibly loc ked into a relationship with a single bank, an interpretation consisten t withthe motivation provided by Rajan (1992).The model generates several predictions that are consistent with the stylized facts. First, weakfirms find it optimal to finance exclusively with bank debt. That is, for weak firms, bank debtdominates any mix of market and bank debt, regardless of the priority structure under the proposedmixed debt policy. This result holds in the absence of any notion of monitoring or certification bybanks, transaction costs, economies of scale, and other common rationales for why small firms failto tap public debt markets. Second, the optimal debt structure for strong firms entails a mixtureof bank and market debt, thus providing a rationale for the coexistence of both types of debt withinthecapitalstructureofasinglefirm. Third, while employing a mixed debt structure, strong firmsoptimally place bank debt senior in priority.To the extent that one views y oung firms as having a weak ex post bargaining position vis-`a-visbanks, and gaining bargaining strength as they mature, the model generates a tax-based life-cyclehypothesis for debt structure. Young firms begin by relying exclusively on bank debt. As theygrow and gain bargaining power, they shift away from bank debt, placing more reliance on marketdebt. This prediction is consistent with observed financing patterns, and is not dependent on bankcertification of y oung firms. In fact, the model predicts that even if a weak firm could tap publicdebt markets with fair pricing, it would be sub-optimal to do so.The intuition for our results is as follows. First, consider optimal debt structure when the firmhas full ex post bargaining power. Bank debt offers the advantage of being renegotiable in badstates, implying lower bankruptcy costs than those associated with market debt. However, thestrong firm has limited bank debt capacity. Since the firm can make take-it-or-leave-it offers to thebank, the initial value of bank debt cannot exceed the bank’s threat poin t in renegotiations, wherethe threat point is equal to bank recoveries in the event of reorganization. In order maximize itsbank